Atmospheric tides and rotation of the Earth

The six-hourly values of the atmospheric angular momentum (AAM) functions computed by the U.S. National Meteorological Center (NMC) were used to estimate the effects of the atmospheric tides on the Earth's rotation. Variations of the equatorial components ₁ and ₂ of the AAM have periods close to gravitational tidesP ₁ andK ₁.The amplitudes of the detected variations in ₁ and ₂ functions have been found to be much larger than the theoretical ones, the reason of this amplification remains unexplained. According to theoretical formulations, these waves can be expressed only as retrograde motions. Because of frame effects, there is a correspondance between diurnal retrograde polar motion and precession-nutations and the atmospheric effect on polar motion cannot be detected from observations.The second part of this paper deals the effects of atmospheric tides in Earth rotation. High-frequency UT1 variations have been derived from VLBI and GPS techniques during the SEARCH'92 campaign (Study ofEarth-AtmosphereRapidCHanges) (Dickey et al. 1994). They have been compared to values derived by Ray et al. (1994) from global ocean tide model. The results obtained in the present paper show the existence of variations of thermal origin with an amplitude of about 1µs in Universal Time UT1. The agreement between observed and theoretical values is better when the determined thermal atmospheric tides are taken into account.Oceanic tidal signal explains a large part (60% of the signal variance) of the diurnal and sub-diurnal variations. Our results show that only a small part of the residuals (5%) accounts for the atmospheric tidal effects. The residual signal remains unexplained; it might be due to mismodelization of oceanic or atmospheric tides or effect of other geophysical phenomena.     

Assimilation of Earth rotation parameters into a global ocean model: length of day excitation

Changes in the oceanic current system and in the oceanic mass distribution alter, together with other processes, the state of the Earth’s rotation. This state is characterized by the length of day (LOD) and the tilt of the pole-to-pole axis. The aim of our study was to derive the respective governing physical mechanisms in the ocean. Therefore, Earth rotation observations were assimilated into a global circulation model of the ocean. Although assimilation is a well-established tool in climate science, the assimilation of Earth rotation observations into a global ocean model was done here for the first time. Prior to the assimilation, the Earth rotation observations were projected onto the angular momentum of the ocean. Non-oceanic contributions were removed. The result of the subsequent assimilation procedure is a time varying ocean model state that reproduces the projected Earth rotation observations well. This solution was studied to understand the oceanic generation of Earth rotation deviations and to identify governing physical mechanisms. This paper focuses on LOD anomalies although polar motion was assimilated simultaneously. Our results indicate that changes in the oceanic LOD excitation are mostly attributed to changes in total ocean mass. Changes in the spatial distribution of ocean mass turned out to have a minor contribution to the LOD deviations. The same applies to changes in the current system.     

Constant part of the Earth tides in the Earth figure theory

Journal of Geodesy - It is recommended not to reduce measured geodetic values by the constant part of the tidal influence. For this case there is shown an exact solution of the tasks of the theory...     

One centimeter-level observations of diurnal ocean tides from global monthly mean time-variable gravity fields

A method of analyzing GRACE satellite-to-satellite ranging data is presented which accentuates signals from diurnal ocean tides and dampens signals from long-period non-tidal phenomena. We form a time series of differences between two independent monthly mean gravity solutions, one set computed from range-rate data along strictly ascending arcs and the other set computed from data along descending arcs. The solar and lunisolar diurnal tides having alias periods longer than a few months, such as K ₁, P ₁, and S ₁, present noticeable variations in the monthly ascending and descending ‘difference’ solutions, while the climate-related signals are largely cancelled. By computing tidal arguments evaluated along the actual GRACE orbits, we decompose and estimate residual tidal signals with respect to our adopted prior model GOT4.7. The adjustment in the tidal height is small yet significant, yielding maximum amplitudes of 4 cm mostly under the Antarctic ice shelves and ~1 cm in general at spatial scales of several hundred kilometer. Moreover, the results suggest there are possible 1-cm errors in the tide model even over oceans well-covered by decades of radar altimetry missions. Independent validation of such small adjustments covering wide areas, however, is difficult, particularly with limited point measurements such as tide gauge.     

Assessment of periodic sub-diurnal Earth rotation variations at tidal frequencies through transformation of VLBI normal equation systems

We present an empirical model for periodic variations of diurnal and sub-diurnal Earth rotation parameters (ERPs) that was derived based on the transformation of normal equation (NEQ) systems of Very Long Baseline Interferometry (VLBI) observing sessions. NEQ systems that contain highly resolved polar motion and UT1-TAI with a temporal resolution of 15 min were generated and then transformed to the coefficients of the tidal ERP model to be solved for. To investigate the quality of this model, comparisons with empirical models from the Global Positioning System (GPS), another VLBI model and the model adopted by the conventions of the International Earth Rotation and Reference Systems Service (IERS) were performed. The absolute coefficients of these models agree almost completely within 7.5 μ as in polar motion and 0.5 μs in UT1-TAI. Several bigger differences exist, which are discussed in this paper. To be able to compare the model estimates with results of the continuous VLBI campaigns, where signals with periods of 8 and 6 h were detected, terms in the ter- and quarter-diurnal band were included in the tidal ERP model. Unfortunately, almost no common features with the results of continuous VLBI campaigns or ERP predictions in these tidal bands can be seen.     

Earth rotation parameter estimation by GPS observations

The methods of Earth rotation parameter （ERP） estimation based on IGS SINEX file of GPS so- lution are discussed in detail. There are two different ways to estimate ERP： one is the parameter transformation method, and the other is direct adjustment method with restrictive conditions. By comparing the estimated results with independent copyright program to IERS results, the residual systemic error can be found in estimated ERP with GPS observations.     

Earth rotation parameter estimation by GPS observations

The methods of Earth rotation parameter (ERP) estimation based on IGS SINEX file of GPS solution are discussed in detail. There are two different ways to estimate ERP: one is the parameter transformation method, and the other is direct adjustment method with restrictive conditions. By comparing the estimated results with independent copyright program to IERS results, the residual systemic error can be found in estimated ERP with GPS observations.     

Determination of high frequency variations in earth's rotation from Doppler satellite observations

The determination of high frequency variations in UT-1 and a component of pole position from a single pass of Doppler observations of a Navy Navigation Satellite is affected by instrument errors and uncertainties in the gravity field and atmospheric drag forces used in computing the satellite orbit. For elevation angles above20°, instrument errors contribute about2 msec to the determination of UT-1 and “.03 to the determination of pole position. Gravity and drag errors contribute about 0“.03 of correlated error. But gravity errors may be inferred by statistical analysis of residuuls after drag errors are reduced by drag-compensating devices aboard future Navy Navigation Satellites. Since20 Doppler stations nominally acquire about100 passes each day, daily observations of UT-1 and pole position could achieve precisions of0.2 msec and “.005, respectively, assuming half the passes contribute to the determination of each component of pole position. The current accuracy of Doppler results for two day solutions is about50 cm for pole position and1 msec for high frequency variations in UT-1.     

Methodology for the combination of sub-daily Earth rotation from GPS and VLBI observations

A combination procedure of Earth orientation parameters from Global Positioning System (GPS) and Very Long Baseline Interferometry (VLBI) observations was developed on the basis of homogeneous normal equation systems. The emphasis and purpose of the combination was the determination of sub-daily polar motion (PM) and universal time (UT1) for a long time-span of 13 years. Time series with an hourly resolution and a model for tidal variations of PM and UT1-TAI (dUT1) were estimated. In both cases, 14-day nutation corrections were estimated simultaneously with the ERPs. Due to the combination procedure, it was warranted that the strengths of both techniques were preserved. At the same time, only a minimum of de-correlating or stabilizing constraints were necessary. Hereby, a PM time series was determined, whose precision is mainly dominated by GPS observations. However, this setup benefits from the fact that VLBI delivered nutation and dUT1 estimates at the same time. An even bigger enhancement can be seen for the dUT1 estimation, where the high-frequency variations are provided by GPS, while the long term trend is defined by VLBI. The estimated combined tidal PM and dUT1 model was predominantly determined from the GPS observations. Overall, the combined tidal model for the first time completely comprises the geometrical benefits of VLBI and GPS observations. In terms of root mean squared (RMS) differences, the tidal amplitudes agree with other empirical single-technique tidal models below 4 μas in PM and 0.25 μs in dUT1. The noise floor of the tidal ERP model was investigated in three ways resulting in about 1 μas for diurnal PM and 0.07 μs for diurnal dUT1 while the semi-diurnal components have a slightly better accuracy.     

An improved empirical model for the effect of long-period ocean tides on polar motion

Because the tide-raising potential is symmetric about the Earth’s polar axis it can excite polar motion only by acting upon non-axisymmetric features of the Earth like the oceans. In fact, after removing atmospheric and non-tidal oceanic effects, polar motion excitation observations show a strong fortnightly tidal signal that is not completely explained by existing dynamical and empirical ocean tide models. So a new empirical model for the effect of the termensual (Mtm and mtm), fortnightly (Mf and mf), and monthly (Mm) tides on polar motion is derived here by fitting periodic terms at these tidal frequencies to polar motion excitation observations that span 2 January 1980 to 8 September 2006 and from which atmospheric and non-tidal oceanic effects have been removed. While this new empirical tide model can fully explain the observed fortnightly polar motion excitation signal during this time interval it would still be desirable to have a model for the effect of long-period ocean tides on polar motion that is determined from a dynamical ocean tide model and that is therefore independent of polar motion observations.     

三轴弹性地球自转的动力学方程

整体地球自转动力学理论一般假设地球是旋转对称的,但实际上地球是一个非对称的旋转椭球体。因此,三轴地球自转的研究是符合现实的。本文在弹性地球自转Liouville方程的基础上,在推导过程中所有量保留到极移平方和椭率乘积量级而忽略其更小量级的情况下,给出了适用于地球自转研究的三轴弹性地球自转的动力学方程。同时也列出了求解三轴弹性地球自转自由摆动的两种方法,即椭圆积分方法和椭圆函数方法。最后指出,如果在推导过程中保留更小量级,则弹性地球模型的自转动力学方程无解析解;旋转对称地球自转的线性解是三轴地球模型在极移量级下的一种特例,且三轴弹性地球模型不可能出现第二自由摆动。     

Prediction of Earth rotation parameters by fuzzy inference systems

The short-term prediction of Earth rotation parameters (ERP) (length-of-day and polar motion) is studied up to 10 days by means of ANFIS (adaptive network based fuzzy inference system). The prediction is then extended to 40 days into the future by using the formerly predicted values as input data. The ERP C04 time series with daily values from the International Earth Rotation Service (IERS) serve as the data base. Well-known effects in the ERP series, such as the impact of the tides of the solid Earth and the oceans or seasonal variations of the atmosphere, were removed a priori from the C04 series. The residual series were used for both training and validation of the network. Different network architectures are discussed and compared in order to optimize the network solution. The results of the prediction are analyzed and compared with those of other methods. Short-term ERP values predicted by ANFIS show root-mean-square errors which are equal to or even lower than those from the other considered methods. The presented method is easy to use.Acknowledgments. The presented study was undertaken during a six-month stay of the first author at the DGFI (Deutsches Geodätisches Forschungsinstitut) in Munich. The authors wish to thank the DAAD (German Academic Exchange Service) for its support of this project. The first author would like to express many thanks to Prof. Dr.-Ing. Hermann Drewes and all other administrative and academic staff at the DGFI for providing a very warm welcome which motivated and encouraged him during his study on this project. The cooperation of Dr.-Ing. Katja Heine (TU Cottbus, Germany) is gratefully acknowledged, in particular her hospitality during the two stays of the first author in Cottbus.     

EARTH ROTATION EQUATIONS CONTAINING BOTH NUTATION AND POLAR MOTION

1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｍｏｄｅｒｎＥａｒｔｈｒｏｔａｔｉｏｎｔｈｅｏｒｙ ,ｔｈｒｅｅｒｅｆｅｒｅｎｃｅｆｒａｍｅｓａｒｅｕｓｕａｌｌｙｕｓｅｄ ,ｉ.ｅ .,ｔｈｅｓｐａｔｉａｌ (ｉｎｅｒｔｉａｌ)ｆｒａｍｅＯξ1 ξ2 ξ3,ｔｈｅｔｅｒｒｅｓｔｒｉａｌｆｒａｍｅＯｘ1 ｘ2 ｘ3ａｎｄｔｈｅｎｕｔａｔｉｏｎｆｒａｍｅＯｘ01 ｘ02 ｘ03.Ｔｈｅｎｕｔａｔｉｏｎｆｒａｍｅｄｅｆｉｎｅｓａｃｅｌｅｓｔｉａｌｅｐｈｅｍｅｒｉｓｐｏｌｅ .Ｔｈｅｍｏｔｉｏｎｏｆｔｈｉｓｃｅｌｅｓｔｉａｌｅｐｈｅｍｅｒｉｓｐｏｌｅｗ…     

Earth rotation and network geometry optimization for very long baseline interferometers

Very Long Baseline Interferometry (VLBI) is one of the new techniques which will probably dominate geodesy and geophysics in the near future. Its main advantage lies in the fact that it brings the accuracy of direction measurements to a level previously possible only for range measurements. This closes the gap between powerful range determination techniques such as laser ranging and the much less accurate determination of directions through photographic tracking of artificial earth satellites. The technique is geometric in the sense that the relevant observations are independent of the gravity field of the earth. However, the “orbits” of the observed extragalactic radio sources with respect to an earth-fixed system are dominated and perturbed by the rotation of the earth with respect to inertial frame. This allows the determination of polar motion, precession-nutation and length-of-the-day variations, and the technique becomes also “dynamic” in this respect. The capability of determining the geometry of a network of stations within a short time interval and with a centimeter level accuracy also allows the study of the variation of network geometry with time caused by earth tides and other periodic or secular station drifts. The main objective of the present work is the exploration of the capabilities of VLBI for the recovery of earth rotation and network geometry parameters. For this purpose, a number of characteristic experimental designs based on present and candidate for the near future station locations is chosen. The results from the analysis of simulated observations for each particular design are presented in the paper. Presented at IAG International Symposium on “Optimization of Design and Computation of Control Networks”, Sopron, Hungary, 4–10 July 1977.     

On the rotation of the Earth and the terrestrial reference system

The Working Group on the Rotation of the Earth was established in 1978 and developed a programme of international collaboration to Monitor Earth-Rotation and Intercompare the Techniques of observation and analysis (MERIT). The MERIT Short Campaign was held in 1980 to test and develop the organisational arrangements required during the MERIT Main Campaign in 1983–4. The Working Group on the Terrestrial Reference System was established in 1980 to prepare a proposal for the establishment and maintenance of a new Conventional Terrestrial Reference System (COTES) that would be based on the new techniques of space geodesy. The Working Groups collaborated closely and organised two intensive campaigns in 1984 and 1985 that were aimed primarily at determining the relationships between the reference systems of the six different techniques that were used to determine earth-rotation parameters. Observational data were obtained from 35 countries; analyses and intercomparisons of the results were carried out in 7 countries. The Working Groups reviewed the results at the Third MERIT Workshop and recommended that a new International Earth Rotation Service be set up in 1988 and that it be based on the use of very-long-baseline radio interferometry and both satellite and lunar laser ranging.     

Shallow-water loading tides in Japan from superconducting gravimetry

Gravity observations from superconducting gravimeters are used to observe loading effects from shallow-water tides on the Japanese east and west coasts. Non-linear third-diurnal and higher-frequency shallow-water tides are identified in the tide-gauge observations from these coastal areas. The most energetic constituents in the tide gauge observations are also seen in the gravity observations due to their loading effects on the deformation of the Earth. Even though the shallow-water tides at the Japanese east coast have an amplitude of only a few millimetres, they are still able to generate a loading signal at gravity sites located several hundred kilometres inland. In particular, the S₃, S₄ and S₅ solar tides occur in both gravity and tide gauge observations. It is indicated that in other shelf regions with large shallow water tides, the shallow water loading signals account for a significant signal, which should be taken into account.Acknowledgement The authors would like to thank the Hydrographic and Oceanographic Department (Japan Coast Guard), Japan Meteorological Agency and Hokkaido Development Agency for access to the tide-gauge data. Also, the Global Geodynamic Project Information System and Data Center (GGP-ISDC) is acknowledged for providing the gravity data.     

Modeling the length of day and extrapolating the rotation of the Earth

The stochastic behavior of the length of day (LOD) process is analyzed and is modeled within statistical accuracy on a time-scale ranging from weeks to millennia by a three-component model comprising a global Brownian motion process, decadal fluctuations, and a 50-day Madden–Julian oscillation. While the model is intended to be phenomenological, some possible physical models underlying the three components are speculated upon. The model is applied to estimate long-range extrapolation errors. For example, it predicts a standard error of 1 h in the clock-time correction ΔT for extrapolation by 1,500 years from 500 to 2000 BC.     

High-resolution atmospheric angular momentum functions related to Earth rotation parameters during CONT08

Due to the temporal resolution of available numerical weather analyses, the effect of the atmosphere on Earth rotation at daily and sub-daily periods is usually investigated using 6-hourly atmospheric angular momentum (AAM) functions. During the period of CONT08, however, atmospheric analysis data were provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) also on an hourly basis. In this paper, we, therefore, determine two sets of AAM functions from ECMWF data—one for CONT08 with hourly resolution and one for the year 2008 with 6-hourly resolution. The comparisons of the AAM functions to high-resolution Earth rotation parameters (ERP) from VLBI and GPS observations are carried out in the frequency domain. Special attention is paid to the preparation of the high-resolution data sets for the geodetic purposes, as there are jump discontinuities at 12 h intervals. Hence, the hourly AAM functions need to be concatenated. The revised functions yield much smaller amplitudes than their 6-hourly counterparts, as can be seen from the equatorial and the axial frequency spectra of atmospheric excitation in Earth rotation. This decrease of spectral power in the hourly AAM functions is found to be associated with a strong counteraction of pressure and wind terms, which originates from atmospheric circulation on short time scales. The results are compared to previous findings published by Brzeziński and Petrov (IERS Tech Note 28:53–60, 2000) based on the data from the U.S. National Centers for Environmental Prediction (NCEP).     

Measuring rapid variations in Earth orientation,geocenter and crust with satellite laser ranging

This analysis was performed with the GEOSAT software developed at NDRE for high-precision analysis of satellite tracking and VLBI data for geodetic and geodynamic applications. To determine the amplitudes of the tidally coherent daily and sub-daily variations in the Earth's orientation, geocenter, and crust, we have analyzed twelve months of SLR tracking data from the LAGEOS I & II and ETALON I & II satellites, obtained between October 1992 and September 1993. Station coordinates and mean geocenter are determined with an accuracy of 1 to 2 cm. Amplitudes of diurnal and semidiurnal variations in UT1, polar motion, and geocenter are determined with a precision of ~2µts, ~20µas, and 1–3 mm in each component. It is demonstrated that it is possible to determine a one-year continuous high-precision series in UT1 using multi-satellite laser ranging.